What is Amplitude?
You may have observed the waves of sound traveling in air, and waves of ripples in water. If you touch the tip of your pencil or pen to the still water of a container, you will notice that the water surface gets disturbed and produces ripples or waves.
Electromagnetic waves like light waves, microwaves, radio waves and x-ray do not require any medium for their propagation. These waves cannot be seen or heard, but these waves exist in nature and are used in many ways, in day-to-day life.
Every type of wave has some amplitude. Amplitude is the maximum displacement of the wave about its mean position. This maximum displacement or amplitude of a wave is measured in terms of the mean position or equilibrium position of the wave.
The diagram below represents the amplitude and wavelength of a wave. Wavelength is the distance between two consecutive crests or two consecutive troughs of a wave. The uppermost or highest position of a wave is called a crest, and the lowermost position of a wave is called a trough. Time period is defined as the time required completing one full cycle of the wave.
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What is Amplitude Formula?
The formula to calculate amplitude is mentioned below:
x = A sin(ωt+ϕ)
Where,
x = displacement of wave, in metres.
A = amplitude of wave, in metres
ω = angular frequency of wave, in radians.
t = time, in seconds.
ϕ = Initial phase, in radians.
Amplitude and Frequency
Frequency is defined as the number of wave cycles which passes a point per second. It is the number of oscillations that occurs in a wave per second. Frequency is inversely proportional to wavelength. So, the higher the frequency, lower will be the wavelength and vice versa.
Wavelength and frequency are related to each other, but amplitude and frequency are completely independent features of a wave. Both amplitude and frequency can be changed, but a change in one parameter doesn't affect the other. A change in frequency doesn't change the amplitude of the wave, and a change in amplitude doesn't change the frequency of the wave.
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The amplitude of a wave cannot be determined by knowing the value of frequency of the wave. Also, the frequency of a wave cannot be determined by knowing the amplitude of the wave.
Amplitude and Frequency of a Ferris Wheel
The oscillatory motion (height of a passenger in this case) in a Ferris wheel, relative to the center of Ferris wheel, given by the function:
F(t) = Asin(ωt+ϕ) + B,
The time period of this cycle is: \[\frac{2\Pi }{\omega }\]
The phase shift of this cycle is given by:
Where,
A = amplitude
B = vertical shift
Amplitude of Sound
Sound is a form of energy by which we can hear. If you strike a bell, it produces sound. You can feel the vibration of the bell, if you touch it. You can notice that the bell is shaking. This to and fro motion of the bell is called vibration.
The amplitude of a wave, (like that of a sound wave) is the measure of the displacement from the mean position. The amplitude of a sound wave is defined as the maximum displacement of the wave from the equilibrium position.
Mathematically, it is the distance between a crest and the equilibrium position of a sound wave.
The sine wave is given by the equation:
y = A sin ω t
Where,
A = amplitude of the wave,
ω = angular frequency of the wave,
t = time taken
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The amplitude of the wave will change depending upon its oscillation. The loudness of a sound wave varies directly in relation to its amplitude. Higher is the amplitude, higher will be the sound. If the amplitude is low, the sound produced will also be less.
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Time Period in Sound
An event is said to be periodic if it occurs repeatedly. The time taken by a sound wave to complete one cycle is called its time period. The time period is inversely proportional to frequency, and is given by:
Time Period = 1/Frequency
Frequency in Sound
The number of oscillations made by the sound wave per second is called its frequency. The SI unit of frequency is hertz, and is denoted by Hz. Frequency describes how many times a particle vibrates when the wave travels through a medium.
Frequency = 1/Period
FAQs on Amplitude Frequency Period Sound
1. What is the amplitude of a sound wave?
The amplitude of a sound wave describes its intensity or power. It is the maximum displacement or distance moved by a point on a vibrating wave from its rest position. In simpler terms, a larger amplitude means a more powerful and louder sound.
2. What does the frequency of a sound wave tell us?
The frequency of a sound wave tells us the number of complete vibrations or cycles it completes in one second. It is measured in Hertz (Hz). A wave with a high frequency has a high pitch (like a whistle), while a wave with a low frequency has a low pitch (like a drum).
3. What is the time period of a sound wave?
The time period is the amount of time it takes to complete one full cycle of a sound wave. It is usually measured in seconds. If a wave has a high frequency, it will have a short time period because the cycles are completed very quickly.
4. How are frequency and time period related to each other?
Frequency and time period have an inverse relationship. This means that as one value goes up, the other goes down. The formula connecting them is: Frequency = 1 / Time Period. Therefore, a wave that has a short time period will always have a high frequency.
5. How does amplitude affect the loudness of a sound we hear?
The amplitude of a sound wave directly determines its loudness. A wave with a larger amplitude carries more energy, which our ears perceive as a louder sound. A wave with a smaller amplitude is perceived as a quieter sound. For example, shouting creates high-amplitude waves, while whispering creates low-amplitude waves.
6. Why does a high-frequency sound have a high pitch?
Pitch is our brain's interpretation of a sound's frequency. When sound waves with a high number of cycles per second (high frequency) reach our ears, our brain processes this rapid vibration as a high-pitched or 'shrill' sound. Conversely, slower vibrations (low frequency) are interpreted as a low-pitched or 'deep' sound.
7. How does sound travel from one place to another?
Sound travels by creating vibrations in a medium like air, water, or solids. When an object vibrates, it pushes and pulls on the particles of the medium next to it. This creates a chain reaction where energy is passed from particle to particle, allowing the sound to propagate as a wave.
8. What are compressions and rarefactions in a sound wave?
As a sound wave travels, it causes the particles of the medium to bunch up and spread out in an alternating pattern.
- Compressions are the regions where the particles are crowded together, creating an area of high pressure.
- Rarefactions are the regions where the particles are spread far apart, creating an area of low pressure.
9. Can sound travel in space? Why or why not?
No, sound cannot travel in the vacuum of space. Sound is a mechanical wave, which means it requires a medium (a substance with particles, like air or water) to travel through. Since space is a vacuum with virtually no particles, there is nothing for the sound vibrations to pass through.
10. What is the main difference between how sound waves and light waves travel?
The main difference lies in their wave type and their need for a medium.
- Sound waves are longitudinal waves where particles vibrate parallel to the wave's direction. They must have a medium to travel.
- Light waves are transverse waves where vibrations are perpendicular to the wave's direction. They are electromagnetic and do not need a medium, which is why light from the sun can reach us through space.
